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This paper deals with the quantification of the different rates in epidemiological models from a function estimation framework, with the objective of identifying the desired unknowns without defining a priori basis functions for describing its behaviour. This approach is used to analyze data for the Covid-19 pandemic in Italy and Brazil. The forward problem is written in terms of the SIRD model, while the inverse problem is solved by combining the Levenberg–Marquardt method with Tikhonov regularization. A very good agreement was achieved between data and the calculated values. The resulting methodology is robust and very versatile, being easily applicable to other epidemiology models and data from other countries. [ABSTRACT FROM AUTHOR]